Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms

TL;DR

This paper provides an exact solution for the open XX quantum spin chain with nondiagonal boundary conditions, deriving eigenvalues and Bethe Ansatz equations using elliptic functions, advancing understanding of integrable quantum models.

Contribution

It introduces a novel Bethe Ansatz solution for the open XX chain with nondiagonal boundaries, including an exact inversion identity and elliptic function formulation.

Findings

Derived eigenvalues of the transfer matrix

Formulated Bethe Ansatz equations for generic boundary parameters

Established a connection with Jacobian elliptic functions

Abstract

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of the boundary parameters, the Bethe Ansatz solution is formulated in terms of Jacobian elliptic functions.